Angular Kinetics After reading this chapter, the student should be able to: Define torque and discuss the characteristics of a torque. State the angular analogs of Newton's three laws of motion and their impact on human movement. Discuss the concept of moment of inertia. Understand the impact of angular momentum on human motion. Define the concept of center of mass. Calculate the segment center of mass and the total body center of mass. Differentiate between the three classes of levers. Discuss the relationships between torque, angular work, rotational kinetic energy, and angular power. Define and conduct a static analysis on a single joint motion. Define stability and discuss its effect on human movement. Define and conduct a dynamic analysis on a single joint motion. Define the impulse-momentum relationship. Define the work-energy relationship.

T=F*r

T=F*r sin ἁ

How torques are commonly generated by muscle force (A), gravitational force (B), and a ground reaction force (C). MA, movement arm.

A wrench with two points of force application. Grasping the wrench at the end (A) generates more torque than a grasp near the point of rotation (B) because the moment arm is greater at A than at B.

Force Couple Force couple=F*d

Newton's Laws of Motion: Angular Analogs A rotating body will continue in a state of uniform angular motion unless acted on by an external torque. Stated mathematically as in the linear If ΣT = 0 then Δω = 0 That is, if the sum of the torques is zero, then the object is either in a state of rest or rotating at a constant angular velocity. First Law: Law of Inertia

The calculation of moment of inertia

Segmental moment of inertia

Second Law: Law of Angular Acceleration An external torque produces an angular acceleration of a body that is proportional to and in the direction of the torque and inversely proportional to the moment of inertia of the body.

local (H L ) and remote (H R ) angular momenta

Center of Mass If the center of mass is the point about which the mass is evenly distributed, it must also be the balancing point of the body. Thus, the center of mass can be further defined as the point about which the sum of the torques equal zero. That is:

Center of Mass Calculation: Segmental Method

Total Body Center of Mass Calculation